-x^2-36=14x+1

Solution for -x^2-36=14x+1 equation:

-x^2-36=14x+1

We move all terms to the left:

-x^2-36-(14x+1)=0

We add all the numbers together, and all the variables

-1x^2-(14x+1)-36=0

We get rid of parentheses

-1x^2-14x-1-36=0

We add all the numbers together, and all the variables

-1x^2-14x-37=0

a = -1; b = -14; c = -37;
Δ = b2-4ac
Δ = -142-4·(-1)·(-37)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{3}}{2*-1}=\frac{14-4\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{3}}{2*-1}=\frac{14+4\sqrt{3}}{-2}
$